Higher Bers maps
The study of Teichmüller spaces is highly topical. A key feature of this theory is that of the Bers embedding. Let \(S\) be a Riemann surface. Then the Bers embedding is a holomorphic map from Teichmüller space \(\mathcal{T}(S)\) to a bounded open subset of the Banach space of holomorphic quadratic differentials on \(S\), equipped with the hyperbolic-supremum norm.NEWLINENEWLINEIn the paper under review, the author studies differential operators on conformal mappings with various other group invariances. In particular, the author gives conditions for such a differential operator to induce a holomorphic map from \(\mathcal{T}(S)\) into a complex Banach space of \(m\)-differentials. The paper contains an extensive survey of the Bers embedding and Teichmüller theory, and concludes by outlining the further work that needs to be done for this approach to have greater impact on Teichmüller theory.
scientific article; zbMATH DE number 6050965